The invention relates to a control process in general and more particularly to a control process for a numerically controlled machine-tool or for a robot.
A control process of this nature is used to determine points along a path which are connected by interpolated motion segments. Taken in their entirety, these motion segments approximate an ideal path of motion for the machine-tool or the robot within a specified tolerance with respect to the position. This ideal path of motion is divided into fine path segments using its point of origin as a first position and its target position as the last position. The characteristic parameters of all the positions on the ideal path of motion are stored and the point of origin is selected as the starting point of the first motion segment.
A process that accomplishes this task is disclosed in the German Published Patent Application 36 23 070. Using this method an ideal path of motion is converted into linear motion segments which can be easily processed by a control system. The end points of these linear motion segments, which meet to form discontinuities, are automatically determined. However, in many applications, these discontinuities that occur along the path of motion are undesirable. In order to protect the mechanisms of either the machine-tool or the robot and in order to obtain an improved surface quality, as well as to obtain a greater feed rate at the workpiece, it would be advantageous if the resulting path exhibited the smoothest possible curve.
A smooth curve can be produced by using a so-called spline method. With the help of a few interpolation points on the ideal path of motion, spline segments can thereby be formed, which, when connected together, yield an extremely smooth curve that approximates the resulting path of motion. For example, such a curve will result if the individual spline segments having the same slope and the same curvature are connected (Werkstatt and Bertribe "Workshop and Factory" 121 (1988) 9, page 737). The individual spline functions are calculated from defined interpolation points or linear sets using standard mathematical methods, such as the method of the natural spline, for example. Examples of this method are found in: "M. Keppeler: Generating Reference Input Variables for Numerically Path-Controlled Industrial Robots, Chapter 2.4.3".
The more complex the paths of motion that are to be travelled and the higher the quality of the results demanded, the shorter the individual spline segments must become. As a result, very large quantities of data are created which need to be processed on-line in the numerical control system. However, large quantities of data necessitate reducing the processing rate of data during execution of the program. This is in conflict with economic and technological requirements, unless hardware is used which is more efficient and is thus also more expensive.
In view of the prior art, there is a need to develop a control process of the type mentioned in the beginning, so that, with the least possible number of spline segments, the ideal path of motion can be approximated while at the same time ensuring that the resulting path of motion only deviates from the ideal path of motion by some maximum limiting value.